Photoelectric effect with n photons

[Dr_Scientist]

So in photoelectric effect, electrons can be ejected from a material when a beam of light shines upon the material, provided that the incident photons have enough energy to overcome the work function, i.e. hbar*omega has to be greater than W.

Now, why can't I have n photons simultaneously hitting on the same electron, therefore giving me energy n*hbar*omega, so that I can virtually knock electrons out from any material with a beam of light of any energy?

 

[Darwin123]

So in photoelectric effect, electrons can be ejected from a material when a beam of light shines upon the material, provided that the incident photons have enough energy to overcome the work function, i.e. hbar*omega has to be greater than W.

Now, why can't I have n photons simultaneously hitting on the same electron, therefore giving me energy n*hbar*omega, so that I can virtually knock electrons out from any material with a beam of light of any energy?

The photoelectric effect can occur with more than one photon hitting at once. The rate of this occurring is proportional to the n1 power of the photon density. However, the rate of multiphoton electron emission is extremely low at the photon densities achievable with lamps or cw lasers. The rate of mutliphoton emission is greater with coherent sources (lasers) then with incoherent sources (lamps) of light.
The nineteenth century physicists examined the photoelectric effect using conventional lamps. The intensity of the light was low. Their electronics were much slower than the advanced electronics that we have today. Because their electronics were so slow, they had to decrease the intensity of their light sources to distinguish between single photon electron emissions. So the photon density of their light sources was extremely low. The rate of single photon electron emission was much larger than the rate of multiphoton electron emission. The “dead-time” problem was big. There was no way a nineteenth century physicist could have detected multiphoton electron emission.
Today, we have high intensity light sources and very fast electronics. So we can detect some multiphoton electron emission. The single photon electron emission is an unwanted background when one want to study two photon electron emission.
Two photon electron emission is enhanced if the two photons are entangled. This is called the two photon effect. Again, physicists of the nineteenth century could not make entangled pairs of photons. So they couldn’t have seen this biphoton enhancement.
Scientists have studied two photon electron emission. I want to contrast a two photon effect without entanglement with a two photon effect without entanglement. Here are two links.

This study does not use biphotons.
http://iopscience.iop.org/1367-2630/9/10/368/
“We report on the observation of two-photon electron emission from silver nanoparticles suspended in nitrogen flow resulting from irradiating them with continuous wave and pulsed laser light with photon energies below the threshold of the single-photon photoelectric effect. The photoelectron yield is quadratic in the light intensity, and the two-photon electron emission threshold is evident.”

The following experiment did not use a high intensity source. They used biphotons.
http://www.maik.ru/full/lasphys/03/12/lasphys12_03p1546full.pdf
“Experimental Observation of the Two-Photon Photoelectric Effect in Faint Biphoton Light
For the first time, the two-photon photoelectric effect in a faint biphoton field was observed experimentally; increased efficiency of the biphoton light as compared to the same intensity of coherent light in the two-photon process was proven.”